B-Integral
Calculate nonlinear phase accumulation and compare it with a caller-defined B-integral limit.
Description
B-integral estimates nonlinear phase accumulation under constant intensity and nonlinear index.
B-integral estimates nonlinear phase accumulation under constant intensity and nonlinear index. The tool compares that calculated phase with a supplied maximum.1
Calculate nonlinear phase accumulation and compare it with a caller-defined B-integral limit.
When to use B-Integral
Use this tool to calculate nonlinear phase accumulation and compare it with a caller-defined B-integral limit.
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 B-Integral 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 wavelengthMeters, nonlinearIndexM2PerW, intensityWPerM2, mediumLengthMeters, maximumBIntegral using the field table and calculation rules, then run the tool.
- Read bIntegralRadians, withinLimit. 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 |
|---|---|---|---|
| wavelengthMeters | Wavelength (m) | number; minimum: 0 | Required |
| nonlinearIndexM2PerW | Nonlinear index (m²/W) | number | Required |
| intensityWPerM2 | Optical intensity (W/m²) | number; minimum: 0 | Required |
| mediumLengthMeters | Medium length (m) | number; minimum: 0 | Required |
| maximumBIntegral | Maximum B-integral (rad) | number; minimum: 0 | Required |
Enter positive wavelength, finite nonlinear coefficient and nonnegative intensity, length and limit. Calculate B and return radians with an inclusive B≤maximum flag. A negative coefficient is accepted by the input contract, but a negative calculated B is rejected by the nonnegative output contract.
B=2π n2 I L/λ; passes if B≤maximum Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| bIntegralRadians | B-integral (rad) | number; minimum: 0 |
| withinLimit | Within limit | boolean |
{
"input": {
"wavelengthMeters": 0.000001,
"nonlinearIndexM2PerW": 3e-20,
"intensityWPerM2": 100000000000000,
"mediumLengthMeters": 0.1,
"maximumBIntegral": 2
},
"output": {
"bIntegralRadians": 1.8849555921538763,
"withinLimit": true
}
}Limitations and assumptions
Use a nonnegative phase basis for successful results. No propagation, polarization, loss or intensity evolution is integrated.
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. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use Brillouin Stokes Cascade: Generate cascaded Brillouin Stokes frequencies from a pump and fixed shift. For a complementary task, use Nonlinear Length: Calculate nonlinear length and accumulated self-phase modulation.
References
-
B-Integral — tool.io
Similar or alternative tools
- Brillouin Stokes Cascade
Generate cascaded Brillouin Stokes frequencies from a pump and fixed shift.
- Nonlinear Length
Calculate nonlinear length and accumulated self-phase modulation.