Focused-Beam Waist Location
Propagate a Gaussian beam q parameter through a thin lens to locate the new waist.
Description
Gaussian q-parameter propagation through a thin lens changes both waist location and Rayleigh range.
Gaussian q-parameter propagation through a thin lens changes both waist location and Rayleigh range. Signed waist-to-lens distance fixes the input geometry convention.1
Propagate a Gaussian beam q parameter through a thin lens to locate the new waist.
When to use Focused-Beam Waist Location
Use this tool to propagate a Gaussian beam q parameter through a thin lens to locate the new waist.
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 Focused-Beam Waist Location 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 inputWaistRadiusMeters, waistToLensDistanceMeters, wavelengthMeters, focalLengthMeters using the field table and calculation rules, then run the tool.
- Read newWaistDistanceAfterLensMeters, newWaistRadiusMeters, rayleighRangeMeters. 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 |
|---|---|---|---|
| inputWaistRadiusMeters | Input waist radius (m) | number; minimum: 0 | Required |
| waistToLensDistanceMeters | Waist-to-lens distance (m) | number | Required |
| wavelengthMeters | Wavelength (m) | number; minimum: 0 | Required |
| focalLengthMeters | Lens focal length (m) | number | Required |
Enter positive waist/wavelength, finite signed distance and nonzero signed focal length. Return −Re(qout) as new waist distance after lens, new radius sqrt(λIm(qout)/π), and Rayleigh range.
zR=πw0²/λ; qin=distance+i zR; qout=1/(1/qin−1/f) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| newWaistDistanceAfterLensMeters | New waist distance after lens (m) | number |
| newWaistRadiusMeters | New waist radius (m) | number; minimum: 0 |
| rayleighRangeMeters | New Rayleigh range (m) | number; minimum: 0 |
{
"input": {
"inputWaistRadiusMeters": 1,
"waistToLensDistanceMeters": 0,
"wavelengthMeters": 3.141592653589793,
"focalLengthMeters": 1
},
"output": {
"newWaistDistanceAfterLensMeters": 0.5,
"newWaistRadiusMeters": 0.7071067811865476,
"rayleighRangeMeters": 0.5
}
}Limitations and assumptions
Negative waist distance describes a waist upstream of the lens in this convention. Ideal Gaussian M²=1 and paraxial thin-lens optics are assumed.
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 Folded-Cavity Astigmatism: Quantify tangential/sagittal waist mismatch in a folded cavity. For a complementary task, use Spatial-Filter Pinhole: Calculate an Airy-diameter spatial-filter pinhole size with relay magnification.
References
-
Focused-Beam Waist Location — tool.io
Similar or alternative tools
- Folded-Cavity Astigmatism
Quantify tangential/sagittal waist mismatch in a folded cavity.
- Spatial-Filter Pinhole
Calculate an Airy-diameter spatial-filter pinhole size with relay magnification.