Figure-Nine Loop Transmission
Calculate idealized complementary-port transmission for a figure-nine nonlinear loop.
Description
A figure-nine loop model uses complementary sine/cosine-squared port fractions.
A figure-nine loop model uses complementary sine/cosine-squared port fractions. Insertion transmission scales only the returned transmitted fraction.1
Calculate idealized complementary-port transmission for a figure-nine nonlinear loop.
When to use Figure-Nine Loop Transmission
Use this tool to calculate idealized complementary-port transmission for a figure-nine nonlinear loop.
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 Figure-Nine Loop Transmission 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 nonlinearPhaseRadians, insertionTransmission using the field table and calculation rules, then run the tool.
- Read reflectingPortFraction, transmittedFraction. 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 |
|---|---|---|---|
| nonlinearPhaseRadians | Loop nonlinear phase (rad) | number | Required |
| insertionTransmission | Insertion transmission | number; minimum: 0; maximum: 1 | Required |
Enter finite signed phase and insertion transmission 0–1. Return reflecting port fraction and scaled transmitted fraction.
reflecting=cos²(phase/2); transmitted=(1−reflecting)×insertion Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| reflectingPortFraction | Reflecting-port fraction | number; minimum: 0; maximum: 1 |
| transmittedFraction | Transmitted fraction | number; minimum: 0; maximum: 1 |
{
"input": {
"nonlinearPhaseRadians": 3.141592653589793,
"insertionTransmission": 0.9
},
"output": {
"reflectingPortFraction": 3.749399456654644e-33,
"transmittedFraction": 0.9
}
}Limitations and assumptions
No coupler imbalance, gain, phase bias or cavity dynamics is included. Outputs do not sum to one when insertion loss is present.
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 Figure-Eight Loop Transmission: Calculate an idealized nonlinear-loop-mirror transmission for a figure-eight cavity. For a complementary task, use Nonlinear Length: Calculate nonlinear length and accumulated self-phase modulation.
References
-
Figure-Nine Loop Transmission — tool.io
Similar or alternative tools
- Figure-Eight Loop Transmission
Calculate an idealized nonlinear-loop-mirror transmission for a figure-eight cavity.
- Nonlinear Length
Calculate nonlinear length and accumulated self-phase modulation.