Resonator Stability

Calculate two-mirror resonator g parameters and test the strict stability interval.

Description

Two-mirror resonator stability uses the product of geometry parameters g=1−L/R.

Two-mirror resonator stability uses the product of geometry parameters g=1−L/R. This tool applies a strict interval and excludes boundary geometries.^[1]

Calculate two-mirror resonator g parameters and test the strict stability interval.

When to use Resonator Stability

Use this tool to calculate two-mirror resonator g parameters and test the strict stability interval.

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 Resonator Stability 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 cavityLengthMeters, firstMirrorRadiusMeters, secondMirrorRadiusMeters using the field table and calculation rules, then run the tool.
Read firstGParameter, secondGParameter, gProduct, stable. 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
cavityLengthMeters	Cavity length (m)	number; minimum: 0	Required
firstMirrorRadiusMeters	First mirror radius (m)	number	Required
secondMirrorRadiusMeters	Second mirror radius (m)	number	Required

Enter positive cavity length and finite nonzero signed mirror radii. Return both g values, their product and strict stability flag.

stable if 0<(1−L/R1)(1−L/R2)<1

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

Output field	Meaning	Value type
firstGParameter	First g parameter	number
secondGParameter	Second g parameter	number
gProduct	G-parameter product	number
stable	Stable resonator	boolean

json

{
  "input": {
    "cavityLengthMeters": 1,
    "firstMirrorRadiusMeters": 2,
    "secondMirrorRadiusMeters": 2
  },
  "output": {
    "firstGParameter": 0.5,
    "secondGParameter": 0.5,
    "gProduct": 0.25,
    "stable": true
  }
}

Limitations and assumptions

Marginal boundaries are false. Plane mirrors cannot be entered as infinity; no astigmatism, thermal lens or mode size is calculated.

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 Cavity Stability: Calculate two-mirror cavity g parameters and geometric stability. For a complementary task, use Folded-Cavity Astigmatism: Quantify tangential/sagittal waist mismatch in a folded cavity.

References

Resonator Stability — tool.io

Similar or alternative tools

Cavity Stability
Calculate two-mirror cavity g parameters and geometric stability.
Folded-Cavity Astigmatism
Quantify tangential/sagittal waist mismatch in a folded cavity.