Dispersion-Map Strength

Calculate net, absolute, and pulse-width-normalized dispersion-map strength.

Description

Dispersion-map strength retains the absolute segment contributions even when their signed sum cancels.

Dispersion-map strength retains the absolute segment contributions even when their signed sum cancels. Pulse-width squared provides a dimensionless normalization.^[1]

Calculate net, absolute, and pulse-width-normalized dispersion-map strength.

When to use Dispersion-Map Strength

Use this tool to calculate net, absolute, and pulse-width-normalized dispersion-map strength.

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 Dispersion-Map Strength 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 segmentDispersionPs2, referencePulseWidthPs using the field table and calculation rules, then run the tool.
Read netDispersionPs2, absoluteDispersionPs2, mapStrength. 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
segmentDispersionPs2	Segment dispersion contributions (ps²)	list of number	Required
referencePulseWidthPs	Reference pulse width (ps)	number; minimum: 0	Required

Enter nonempty finite signed segment dispersions in ps² and positive reference pulse width ps. Return net, absolute and strength.

net=Σsegment; absolute=Σ|segment|; strength=absolute/widthPs²

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

Output field	Meaning	Value type
netDispersionPs2	Net map dispersion (ps²)	number
absoluteDispersionPs2	Sum of absolute dispersion (ps²)	number; minimum: 0
mapStrength	Normalized dispersion-map strength	number; minimum: 0

json

{
  "input": {
    "segmentDispersionPs2": [
      2,
      -1.5
    ],
    "referencePulseWidthPs": 0.5
  },
  "output": {
    "netDispersionPs2": 0.5,
    "absoluteDispersionPs2": 3.5,
    "mapStrength": 14
  }
}

Limitations and assumptions

Segments are already integrated dispersion values; no extra length multiplication is applied. Pulse propagation and width-convention choice are not 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 Net Dispersion: Sum segment dispersion-length products and report the net dispersion sign. For a complementary task, use GDD Ripple: Summarize dispersive-mirror group-delay-dispersion ripple.

References

Dispersion-Map Strength — tool.io

Similar or alternative tools

Net Dispersion
Sum segment dispersion-length products and report the net dispersion sign.
GDD Ripple
Summarize dispersive-mirror group-delay-dispersion ripple.