XPM Phase Shift

Calculate cross-phase index change and nonlinear phase shift.

Description

Cross-phase modulation represents a probe’s refractive-index change caused by another copropagating field.

Cross-phase modulation represents a probe’s refractive-index change caused by another copropagating field. This model uses a fixed factor of two relative to the nonlinear index coefficient.^[1]

Calculate cross-phase index change and nonlinear phase shift.

When to use XPM Phase Shift

Use this tool to calculate cross-phase index change and nonlinear phase shift.

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 XPM Phase Shift 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 nonlinearIndexM2PerW, copropagatingIntensityWPerM2, interactionLengthMeters, probeWavelengthMeters using the field table and calculation rules, then run the tool.
Read indexChange, nonlinearPhaseRadians. 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
nonlinearIndexM2PerW	Nonlinear refractive index (m²/W)	number	Required
copropagatingIntensityWPerM2	Copropagating intensity (W/m²)	number; minimum: 0	Required
interactionLengthMeters	Interaction length (m)	number; minimum: 0	Required
probeWavelengthMeters	Probe wavelength (m)	number; minimum: 0	Required

Enter finite signed nonlinear coefficient, nonnegative intensity and length and positive probe wavelength in SI units. Return signed index and phase changes.

Δn=2n2I; phase=2πΔnL/λ

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

Output field	Meaning	Value type
indexChange	Cross-phase index change	number
nonlinearPhaseRadians	Cross-phase shift (rad)	number

json

{
  "input": {
    "nonlinearIndexM2PerW": 0.5,
    "copropagatingIntensityWPerM2": 1,
    "interactionLengthMeters": 1,
    "probeWavelengthMeters": 6.283185307179586
  },
  "output": {
    "indexChange": 1,
    "nonlinearPhaseRadians": 1
  }
}

Limitations and assumptions

Polarization, temporal overlap, dispersion and depletion are not modeled.

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 Nonlinear Length: Calculate nonlinear length and accumulated self-phase modulation. For a complementary task, use Kerr-Gate Suppression: Measure Kerr-gate background suppression, desired-signal transmission, and SNR improvement.

References

XPM Phase Shift — tool.io

Similar or alternative tools

Nonlinear Length
Calculate nonlinear length and accumulated self-phase modulation.
Kerr-Gate Suppression
Measure Kerr-gate background suppression, desired-signal transmission, and SNR improvement.